Differential Geometry and Lie Groups: A Computational Perspective, Gallier Jean, Quaintance Jocelyn
Автор: Vargas Jose G Название: Differential Geometry for Physicists and Mathematicians ISBN: 981456639X ISBN-13(EAN): 9789814566391 Издательство: World Scientific Publishing Рейтинг: Цена: 105600.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative -- almost like a story being told -- that does not impede sophistication and deep results.It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter.In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose.
Название: Differential Geometry through Supersymmetric Glasses ISBN: 9811206775 ISBN-13(EAN): 9789811206771 Издательство: World Scientific Publishing Рейтинг: Цена: 116160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Back in 1982, Edward Witten noticed that classical problems of differential geometry and differential topology such as the de Rham complex and Morse theory can be described in a very simple and transparent way using the language of supersymmetric quantum mechanics. Since then, many research papers have been written on this subject. Unfortunately not all the results in this field known to mathematicians have obtained a transparent physical interpretation, even if this new physical technique has also allowed many mathematical results to be derived which are completely new, in particular, hyper-Kaehler and the so-called HKT geometry. But in almost 40 years, no comprehensive monograph has appeared on this subject. So this book written by an expert in supersymmetric quantum field theories, supersymmetric quantum mechanics and its geometrical applications, addresses this yearning gap.
It comprises three parts: The first, GEOMETRY, gives basic information on the geometry of real, complex, hyper-Kaehler and HKT manifolds, and is principally addressed to the physicist. The second part "PHYSICS" presents information on classical mechanics with ordinary and Grassmann dynamics variables. Besides, the author introduces supersymmetry and dwells in particular on the representation of supersymmetry algebra in superspace. And the last and most important part of the book "SYNTHESIS", is where the ideas borrowed from physics are used to study purely mathematical phenomena.
Автор: Aldrovandi Ruben & Pereira Jose Geraldo Название: Introduction To Geometrical Physics, An (Second Edition) ISBN: 981314680X ISBN-13(EAN): 9789813146808 Издательство: World Scientific Publishing Цена: 285120.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
"The book contains a very large amount of material and is useful for students and specialists as a reference book."
Zentralblatt MATH
This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature -- gravitational, electromagnetic, strong nuclear, and weak nuclear.
The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students.
In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.
Автор: Vladimir D. Liseikin Название: A Computational Differential Geometry Approach to Grid Generation ISBN: 3642070620 ISBN-13(EAN): 9783642070624 Издательство: Springer Рейтинг: Цена: 113180.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The process of breaking up a physical domain into smaller sub-domains, known as meshing, facilitates the numerical solution of partial differential equations used to simulate physical systems.
Автор: Chen Bang-yen Название: Differential Geometry Of Warped Product Manifolds And Submanifolds ISBN: 9813208929 ISBN-13(EAN): 9789813208926 Издательство: World Scientific Publishing Рейтинг: Цена: 174240.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry -- except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The notion of warped product manifolds plays very important roles not only in geometry but also in mathematical physics, especially in general relativity. In fact, many basic solutions of the Einstein field equations, including the Schwarzschild solution and the Robertson-Walker models, are warped product manifolds.
The first part of this volume provides a self-contained and accessible introduction to the important subject of pseudo-Riemannian manifolds and submanifolds. The second part presents a detailed and up-to-date account on important results of warped product manifolds, including several important spacetimes such as Robertson-Walker's and Schwarzschild's.
The famous John Nash's embedding theorem published in 1956 implies that every warped product manifold can be realized as a warped product submanifold in a suitable Euclidean space. The study of warped product submanifolds in various important ambient spaces from an extrinsic point of view was initiated by the author around the beginning of this century.
The last part of this volume contains an extensive and comprehensive survey of numerous important results on the geometry of warped product submanifolds done during this century by many geometers.
Автор: Yekutieli Amnon Название: Nonabelian Multiplicative Integration On Surfaces ISBN: 9814663840 ISBN-13(EAN): 9789814663847 Издательство: World Scientific Publishing Рейтинг: Цена: 61250.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Nonabelian multiplicative integration on curves is a classical theory. This volume is about the 2-dimensional case, which is much more difficult.
Автор: Aldrovandi Ruben & Pereira Jose Geraldo Название: Introduction To Geometrical Physics, An (Second Edition) ISBN: 9813146818 ISBN-13(EAN): 9789813146815 Издательство: World Scientific Publishing Цена: 77090.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
"The book contains a very large amount of material and is useful for students and specialists as a reference book."
Zentralblatt MATH
This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature -- gravitational, electromagnetic, strong nuclear, and weak nuclear.
The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students.
In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.
Автор: Urakawa, Hajime (tohoku Univ, Japan) Название: Geometry of biharmonic mappings: differential geometry of variational methods ISBN: 9813236396 ISBN-13(EAN): 9789813236394 Издательство: World Scientific Publishing Рейтинг: Цена: 121440.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 'The present volume, written in a clear and precise style, ends with a rich bibliography of 167 items, including some classical books and papers. In the reviewer (TM)s opinion, this excellent monograph will be a basic reference for graduate students and researchers working in the field of differential geometry of variational methods.'zbMATHThe author describes harmonic maps which are critical points of the energy functional, and biharmonic maps which are critical points of the bienergy functional. Also given are fundamental materials of the variational methods in differential geometry, and also fundamental materials of differential geometry.
The Moment-SOS hierarchy is a powerful methodology that is used to solve the Generalized Moment Problem (GMP) where the list of applications in various areas of Science and Engineering is almost endless. Initially designed for solving polynomial optimization problems (the simplest example of the GMP), it applies to solving any instance of the GMP whose description only involves semi-algebraic functions and sets. It consists of solving a sequence (a hierarchy) of convex relaxations of the initial problem, and each convex relaxation is a semidefinite program whose size increases in the hierarchy.
The goal of this book is to describe in a unified and detailed manner how this methodology applies to solving various problems in different areas ranging from Optimization, Probability, Statistics, Signal Processing, Computational Geometry, Control, Optimal Control and Analysis of a certain class of nonlinear PDEs. For each application, this unconventional methodology differs from traditional approaches and provides an unusual viewpoint. Each chapter is devoted to a particular application, where the methodology is thoroughly described and illustrated on some appropriate examples.
The exposition is kept at an appropriate level of detail to aid the different levels of readers not necessarily familiar with these tools, to better know and understand this methodology.
Автор: Rafael Ortega Название: Periodic Differential Equations in the Plane: A Topological Perspective ISBN: 3110550407 ISBN-13(EAN): 9783110550405 Издательство: Walter de Gruyter Цена: 123910.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Periodic differential equations appear in many contexts such as in the theory of nonlinear oscillators, in celestial mechanics, or in population dynamics with seasonal effects. The most traditional approach to study these equations is based on the introduction of small parameters, but the search of nonlocal results leads to the application of several topological tools. Examples are fixed point theorems, degree theory, or bifurcation theory. These well-known methods are valid for equations of arbitrary dimension and they are mainly employed to prove the existence of periodic solutions. Following the approach initiated by Massera, this book presents some more delicate techniques whose validity is restricted to two dimensions. These typically produce additional dynamical information such as the instability of periodic solutions, the convergence of all solutions to periodic solutions, or connections between the number of harmonic and subharmonic solutions. The qualitative study of periodic planar equations leads naturally to a class of discrete dynamical systems generated by homeomorphisms or embeddings of the plane. To study these maps, Brouwer introduced the notion of a translation arc, somehow mimicking the notion of an orbit in continuous dynamical systems. The study of the properties of these translation arcs is full of intuition and often leads to "non-rigorous proofs". In the book, complete proofs following ideas developed by Brown are presented and the final conclusion is the Arc Translation Lemma, a counterpart of the Poincare–Bendixson theorem for discrete dynamical systems. Applications to differential equations and discussions on the topology of the plane are the two themes that alternate throughout the five chapters of the book.
Автор: Javier de Lucas, Cristina Sardon Munoz Название: A Guide to Lie Systems with Compatible Geometric Structures ISBN: 1786346974 ISBN-13(EAN): 9781786346971 Издательство: World Scientific Publishing Рейтинг: Цена: 142560.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.
Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.
This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer-Cartan form, and the Lie derivative are covered.
Readers will find useful applications to special and general relativity, Yang-Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry.
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